Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4, -1)?

Answer 1

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Answer 2

`D(7,3) \\ E(8,1) \\ F(4,-1)`

The lengths of the sides of the triangle:

`\overline{DE}=√((8-7)^2+(1-3)^2)=√(1^2+(-2)^2)=√(1+4)=√(5) \\ \\ \overline{DF}=√((4-7)^2+(-1-3)^2)=√((-3)^2+(-4)^2)=√(9+16)=√(25)=5 \\ \\ \overline{EF}=√((4-8)^2+(-1-1)^2)=√((-4)^2+(-2)^2)=√(16+4)=√(20)= \\ =√(4 * 5)=2√(5)`

No sides are equal to each other, so it's a scalene triangle.

Check if the sides satisfy the Pythagorean theorem:

`(√(5))^2 + (2√(5))^2=5^2 \\ 5+20=25 \\ 25=25 \\ true`
They do, so it's a right triangle.

The triangle is a right scalene triangle.